Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bhbb)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-29/8, b>=a

For fixed z and a=-29/8, b=47/8

http://functions.wolfram.com/07.23.03.bhbb.01

Input Form

Hypergeometric2F1[-(29/8), 47/8, -(11/2), -z] == (1/(96374784 (1 + z)^(59/8))) ((96374784 + 310480128 z + 186064480 z^2 - 128173871 z^3 + 134185887 z^4 - 190691137 z^5 + 701190581 z^6 + 6163043940 z^7 + 11661737472 z^8 + 10123846656 z^9 + 4314562560 z^10 + 735313920 z^11) Cos[(3 ArcTan[Sqrt[z]])/4] - Sqrt[z] (-72281088 - 222319104 z - 109542468 z^2 + 105811339 z^3 - 116914175 z^4 + 163699809 z^5 + 3679317327 z^6 + 7800218976 z^7 + 7151139072 z^8 + 3155496960 z^9 + 551485440 z^10) Sin[(3 ArcTan[Sqrt[z]])/4])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]